New Correlation for Predicting Undersaturated Oil Compressibility for Mishrif Reservoir in the Southern Iraqi Oil Fields

Reservoir fluids properties are very important in reservoir engineering computations such as material balance calculations, well testing analyses, reserve estimates, and numerical reservoir simulations. Isothermal oil compressibility is required in fluid flow problems, extension of fluid properties from values at the bubble point pressure to higher pressures of interest and in material balance calculations (Ramey, Spivey, and McCain). Isothermal oil compressibility is a measure of the fractional change in volume as pressure is changed at constant temperature (McCain). The most accurate method for determining the Isothermal oil compressibility is a laboratory PVT analysis; however, the evaluation of exploratory wells often require an estimate of the fluid behavior prior to obtaining a representative reservoir sample. Also, experimental data is often unavailable. Empirical correlations are often used for these purposes. This paper developed a new mathematical model for calculating undersaturated oil compressibility using 129 experimentally obtained data points from the PVT analyses of 52 bottom hole fluid samples from Mishrif reservoirs in the southern Iraqi oil fields. The new undersaturated oil compressibility correlation developed using Statistical Analysis System (SAS) by applying nonlinear multiple regression method. It was found that the new correlation estimates undersaturated oil compressibility of Mishrif reservoir crudes in the southern Iraqi oil fields much better than the published ones. The average absolute relative error for the developed correlation is 7.16%.


INTRODUCTION
Al-Marhon reported an average absolute relative error of 5.46%.
In 2008, Al-Aboodi developed new correlation for oil compressibility for the south Iraqi oils using non-linear regression method.
The average absolute relative error is 6.13%.

DATA DESCRIPTION
The data used in this study were obtained from Mishrif reservoir for several southern Iraqi oil fields.

NOMENCLATURE
Reservoir fluid properties form one of the many bases in petroleum engineering calculations.The evaluation of oil and gas reserves, fluid flow through porous media, and multiphase flow in pipes, surface and subsurface equipment design, and production system optimization are strongly depending on reservoir fluid physical properties.Those properties may be measured experimentally in a PVT (pressure-volume-temperature) laboratory or they may be estimated by using empirical correlations.The most accurate method for determining the behavior of these fluids is a laboratory PVT analysis; however, the evaluation of exploratory wells and the advanced design of equipment often require an estimate of the fluid behavior prior to obtaining a representative reservoir sample.Also, experimental data is often unavailable in reservoirs which do not warrant the cost of an in depth fluid study.Empirical correlations are often used for such purposes.The isothermal oil compressibility at pressure above the bubble point is defined as the fractional change in volume of oil as pressure is changed at constant temperature (Ahmed).For crude oil system, the isothermal compressibility coefficient of the oil phase C o is defined, for pressure above the bubblepoint, by one of the following equivalent expression reservoir temperature T, API gravity, gas specific gravity γ g and reservoir pressure.They used 4036 experimental data points and linear regression model to develop the new correlation.In1985, Ahmed used 245 experimental data points to propose a mathematical expression for the isothermal oil compressibility using the gas solubility R S as the only correlation parameter.In 1993 Petrosky and Farshad developed a new correlation for undersaturated isothermal oil compressibility using 304 data points obtained from the Gulf of Mexico crude oils.This new correlation introduces one additional fitting parameter to the model functional form used by Vasquez and Beggs in order to increase the accuracy of the correlation.In 1994, De Ghetto et.al.evaluated the reliability of some isothermal oil compressibility correlations and came up with some modified correlations which they reported as being more accurate.They characterized the fluid samples used in their studies as extra heavy oil (API≤10), heavy oil (10< API≤22.3),medium oil (22.3<API≤31.1) and Light oil (API>31.1).They reported that the errors on the correlation were decreased by about five percent.In 2001, Dindoruk and Christman proposed a new correlation for estimating undersaturated oil compressibility for the Gulf of Mexico.The proposed oil compressibility correlation predicts the oil compressibility values with an average absolute relative error of 186 Middle East PVT reports.
results of the new undersaturated oil compressibility correlation as compared with the other published correlations.In comparison with other known correlations the new undersaturated oil compressibility correlation gives lowest values of average absolute percent relative error (AAERR) and standard deviation (SD) of 7.16 percent and 8.8 percent respectively.A lower value of (AAERR) and (SD) indicate better accuracy of the correlation.The correlation coefficient is 0.89.This shows that the new correlation predicts better undersaturated oil compressibility for Mishrif reservoir crude oil in the southern Iraqi oil fields than any other known correlations.The cross plot in Figure (1) shows acceptable agreement between the measured and the estimated undersaturated oil compressibility using the new correlation.The other correlation results are show in figures (newly developed correlation outperforms the existing ones based on the low value of average absolute percent relative error and standard deviation. E r = Average percent relative error, %.E a = Average absolute percent relative error%.FVF = Formation Volume Factor GOR = Gas-Oil Ratio, SCF/STB.P = Pressure above bubble point, psia Pb = Bubble point pressure, psia.P sep = Separator pressure, psia.R = Coefficient of Correlation, %.Rsb = Solution GOR at bubble point SCF/STB T = Reservoir temperature, R, F. V=Volume, m 3 , cm 3 , ft 3 .γ g = Gas specific gravity (air=1) γ o = Oil specific gravity γ API = Oil API gravity.γ gs = Gas specific gravity at separator pressure γ ob = Oil specific gravity at bubble point PVT = Pressure-Volume-Temperature SAS = Statistical Analysis System =Standard Deviation SD

Hussain Ali Baker New Correlation for Predicting Undersaturated Mrs.Dunia Abdulsaheb Al-Shamma'a Oil Compressibility for Mishrif Reservoir in the Emad Abdulhussain. Fakher Southern Iraqi Oil Fields
Table (1) presents the Dr.

Table ( 3
) shows the statistical error analysis

Table 2 -
Regression Coefficients for the Proposed Undersaturated Oil Dr.